Assessing the Impact of Speed-Limit Increases on Fatal Interstate Crashes

Assessing the Impact of Speed-Limit Increases on Fatal Interstate Crashes

Abstract

This study investigates the relationship between speed-limit increases and increases
in the number of fatal crashes on U.S. rural and urban interstates. Past studies use
expected historical trends to support claims that "speed kills." Using structural modeling,
we assess the change in the average of the time series after a known change in speed
limit occurs. The analysis is carried out separately for urban and rural interstates
for each state. The results cast doubt on the blanket claim that higher speed limits
and higher fatalities are directly related. After the initial speed-limit increases in
1987, the number of fatal accidents on rural interstates increased in some states but
not in all. The 1995 round of speed-limit increases generally showed smaller increases
in fatalities on rural interstates and slight to no increase on urban interstates. The
approach also allows identification of seasonal effects that vary across the states.

Introduction

The relationship between the speed limit and the number of traffic-related fatalities
is a subject of great interest to insurance companies, to the government at all levels,
and to the general public. Historically, the government has taken an active role in the
determination of speed limits, starting with the establishment of the National Maximum
Speed Limit (NMSL) by Congress in January of 1974. Prior to this legislation's setting
the maximum speed limit at 55 miles per hour (mph), many states posted limits as high
as 70 to 75 mph. In April of 1987, Congress passed legislation allowing states to
increase speed limits to 65 mph on qualifying sections of interstate highways in
rural areas with populations of less than 50,000. Within a few months, 38 states
raised the speed limits on appropriate roads. More recently, the National Highway
System (NHS) Designation Act of 1995 was signed into law on November 28, 1995. This
act ended the federal government's involvement in the establishment of speed limits,
putting the responsibility for speed-limit designation and compliance in the hands of
the state governments. In most cases, state governments exercised their new rights and
raised speed limits on rural and urban interstates.

The purpose of this study is to investigate the relationship between speed
limits and traffic-related fatalities. Specifically, we aim to answer the
question Does an increase in the speed limit result in a higher incidence of
fatal crashes? Using a technique known as structural modeling, we are able to
determine the impact speed-limit changes in the past have had on the number of
fatal crashes on rural and urban interstates for each state based on its own past
experiences. This method also gives information about the seasonal patterns in the
number of fatal crashes.

The paper is organized as follows. The next section provides a review of the
literature on the effects of speed-limit increases on the number of traffic-related
crashes and fatalities. The third section presents the data and methodology used in
this study. The fourth section demonstrates the analysis on a single state, and the
fifth describes the results of the study for all states. The final section gives
conclusions and perspectives for future work.

Literature Review

Various studies have attempted to determine the impact of speed-limit
increases on the number of traffic-related crashes and fatalities. The following
is a representative selection of the studies that motivated the study presented in this paper.

The report to Congress entitled "Effects of the 65 mph Speed Limit Through 1990" by the
U.S. Department of Transportation (USDOT), National Highway Traffic Safety Administration
(NHTSA) in May of 1992 looks at yearly interstate-fatality data split by rural and urban
roadways. The analysis is based on "expected historical trends" (USDOT NHTSA 1992). These
projected counts were derived from statistical models based on the historical relationship
between rural-interstate fatalities and fatalities on other roadways. These results do not
convey the impact of the speed-limit increase on traffic fatalities. Rather, the study
relates interstate deaths to noninterstate deaths; it also assumes a stationary, or
nonchanging, environment by fitting a global regression model. The authors then compare
fatalities in 1986 with those in 1990 by computing percentage changes. This approach
ignores historical trends and possible aberrant observations.

The paper does caution that care ought to be taken when interpreting the data. The
authors note that results of individual states probably can not be generalized to the
entire nation. They also point out that no statistical model is capable of controlling
all factors affecting fatalities.

A 1997 paper entitled "Effect of 1996 Speed-Limit Changes on Motor Vehicle Occupant
Fatalities" by Farmer, Retting, and Lund analyzes the effect speed-limit increases during
and around 1996 had on interstates. This study employed linear regression models on trend
and dummy variables to analyze the number of fatalities in states categorized by the time
of their 1996 speed-limit increase (early, late, or none) and compares observed fatalities
with projected values based on historical trends. They use percentage change between 1995
and 1996 to assess the impact of the 1996 legislation. They continually note that vehicle-miles
traveled (VMT) may be able to explain the increase in fatalities but that the appropriate
data are not available.

This study notes that while the national fatality toll for 1996 changed very little
compared with 1995, the change in the fatality toll for individual states varied markedly
between significant decreases and increases. The study also states that total interstate
fatalities increased for the 11 states that had increased speed limits. The authors note
that there has been an increase in the portion of the fatalities occurring on roads
posted at 55 mph or greater and that some increase in fatalities on interstates is to be
expected. Overall, this study presents a very thorough before and after comparison using
percentage changes. A linear trend model with an intervention variable is used to compare
actual 1996 fatalities with estimated 1996 fatalities based on historical trends. The
restriction to annual data and the use of nonadaptive trends limit the value of the comparisons.

"The Effect of Increased Speed Limits in the Post-NMSL Era" is the title of another
National Highway Traffic Safety Administration report to Congress (USDOT NHTSA 1998).
This 1998 study also investigates the effect of the 1995 to 1996 speed-limit increases
on rural and urban interstates.1 It groups states into "changers" (12 count)
and "nonchangers" (18 count) where the latter serve as a comparison for the former. The
authors modeled the logarithms of fatality counts for each year during 1990 to 1996 as
functions of time and type of state. Both linear and quadratic time variables were included.
The impact of the speed increase was modeled using a dummy variable equal to one in 1996 and
zero in previous years. They also included an interaction term between state group and the
1996 indicator to represent the difference between pre-1996/1996 changes for the two state
types while accounting for the time trend. The authors claim that if this interaction term
is significant, the 1996 departure from the time trend among the states that increased
limits differs from the comparison states. The foremost problem with this analysis is
that linear and quadratic trend models are not appropriate for these series. Including
a quadratic trend may lower the residual variance for the in-sample fit, but it will
damage the predictive ability of the model. Inspecting plots of the number of fatalities
or fatal crashes shows that the addition of a global quadratic trend term typically does
not provide a reasonable description for the whole length of the series.

Ledolter and Chan's article "Evaluating the Impact of the 65-mph Maximum Speed Limit
on Iowa Rural Interstates" (1996) examines whether a significant change in the fatal and
major-injury accident rates can be detected following the implementation of a higher speed
limit on rural interstates in Iowa. The authors have access to quarterly data on traffic
speed, traffic volume, and traffic safety. To answer the posed question, they fit a
time-series intervention model relating number of accidents to traffic volume. They
also include time trend, intervention variables for the May 1987 change, and quarterly
seasonality. The authors find that expected numbers of fatal accidents in Iowa rose by
two incidents per quarter on rural interstates, a statistically significant increase.

The data used in the present study are the number of fatal crashes for each
month from January 1975 to December 1998 for each state separated by rural and urban
interstates. We used fatal crashes rather than number of deaths since we regard the
accident data as a more reliable guide to road safety conditions. The number of fatal
crashes was determined from the Fatality Analysis Reporting System (FARS) and is publicly
available3 and maintained by NHTSA. FARS provides monthly data on numbers
of fatal crashes for each state with separate counts for rural and urban interstates.

We let yt denote the number of fatal crashes that occur in
month t and use time series models to examine the impact of an increase in
speed limit on the number of fatal crashes. That is, we are mainly concerned with the
modeling aspect of time series analysis, looking backwards in time for structural
changes in the series. Since the accident data are collected over time in regularly
spaced intervals and the timing of speed-limit changes is known, we use intervention
analysis to examine these effects.

Intervention analysis is a time series technique used when a change in the environment
occurs at a known time and affects the phenomenon of interest.4
In this case, the known change is the speed limit. Since the change in speed limit is more or less
permanent, a step intervention is most appropriate. We hypothesize that the change in
speed limit results in a permanent shift in the number of accidents. To aid in the analysis
and interpretation, we employ the logarithmic transformation. The use of logarithms allows
us to consider percentage changes rather than absolute shifts and stabilizes the variance
of the series. Since some of the months have zero fatal crashes, it is necessary to add
one to each month prior to transforming the data. Thus, it is important to remember when
looking at the plots of the data, as
in figure 1(a), that the series is shifted up by one unit.

Motivated by some of the previous studies on this topic already discussed, we chose to
employ a statistical modeling technique that could provide us with an explanation of the
main features of the phenomena under investigation. Harvey and Durbin (1986) used
structural time-series modeling to examine the effects of seat-belt legislation on
British road casualties. In structural time-series modeling, models are set up
explicitly in terms of the components of interest, such as trends, seasonals, and
cycles. In addition, instead of assuming that these components remain constant over
time, this approach allows them to evolve. The approach is intuitively appealing since
environments that generate time series often do not remain constant and an explicit
description of how these components change can provide valuable insights.

The starting point for the construction of structural models is to represent an
observed value as the sum of level, seasonal, and irregular components.

where yt, as previously defined, is the observation made at
time t, which in our case is after a log
transformation
and and
are
the level, seasonal, and irregular components. In this study, the level component is allowed to
change according to a random walk process, and the seasonal component changes according
to a trigonometric model. That is,

where, with s even (equal to 12 in this case)
and

and where the and
the are
both and are independent of each other. This
formulation allows the seasonal effects to vary over time.

It is possible to include a trend component within the level, but no such
structure was found in any of the data used for this study, so it was omitted.
Finally, in this study we are interested in testing whether a change in the
speed limit results in a permanent change in the level of the number of fatal
crashes for a given state on a given class of interstate. Thus, we can accommodate
this type of analysis by extending the structural model to the form

where
and are
mutually independent of each other, and each has zero mean
and constant variance and is also serially independent. Formally, we write this as

and

We refer to zt as the intervention variable, defined as:

Thus, zt takes on a value of zero up until
time the month
and year of the known speed limit change. The overall fit of the model might be
improved by searching for possible interventions rather than pre-specifying their
timing. Indeed, there may be a time lag before drivers adapted to the new limits.
We decided to retain the more conservative strategy of using the timing of the
legal changes and considering only pure level shifts at those times. With regard
to potential time lags, the variables defined by equation (5) would differ for only
one or two months. If a substantial effect exists, it would still be detected. As
for the host of other potential interventions, we preferred to focus solely on the
impact of speed-limit changes and to avoid concerns about mining the data. When the
component parameters of the structural model are estimated, the intervention
parameter
can be used to assess the impact of the speed-limit change. The
value approximates the
percentage increase in the number of fatal crashes after the speed limit was exposed.
The exact value is more complex as a result of using the transformation
ln(xt + 1) rather than ln(xt); the differences
are slight unless the mean level is very low when percentage changes are rather
unreliable anyway. The computer package STAMP 5.0, developed by Harvey and his
associates, was used to perform the analyses presented in this study.

Example: Rural Arizona

As an example of this method of analysis, consider rural interstates in Arizona.
The speed limit was changed in April 1987 and December 1995. Thus, an intervention
variable was specified for each of these months, defined as in equation (5). The
original time series is shown in figure 1(a).

The series is decomposed into level, seasonal, and irregular components represented
graphically in figure 1, panels a, b, and c, after transformation back to the original
units. We see a significant increase in the level around 1987 but none around 1995.
This indicates that around 1987 the average number of fatal crashes significantly
increased, but not so elsewhere. This increase occurs at the same time as a speed-limit
increase. Statistically, it is estimated that the 1987 speed-limit increase resulted
in a 41% increase in rural interstate crashes in Arizona
(see table 1). There is no
statistical evidence that the 1995 speed-limit increase had any additional effect on
the number of fatal crashes. This may change as more observations become available,
better defining the impact of the policy change.

Next, we see from the seasonal component that there appears to be a strong monthly
effect on the number of fatal crashes. For this example, there are considerably more
crashes in June, July, and August compared with the other months. Such seasonal patterns
exist for most states and reflect the higher traffic levels in summer months. The
irregular component is simply what is left over after the level and seasonal components
are taken into account.

The Structural Time Series Modeling approach tells us that there is a strong seasonal
effect on the number of fatal crashes and that there is a significant increase in the
number of such crashes around the time the speed limit was changed. For this particular
series, the plot of the level component suggests that, after the initial jolt of the
speed-limit change, the trend gradually moves back to its original level. This
phenomenon was observed for a number of states, but not all. Such a movement would
be consistent with the slight overall decline in fatal accidents nationally over this
time period, as shown in figure 2. This observation is made tentatively, since partial
adjustment effects were neither modeled nor tested. The picture is further complicated
as state laws were enacted at different times. Nevertheless, we view this as a question
worthy of further exploration since several distinct hypotheses exist, with quite
different policy implications. Such hypotheses include 1) drivers adjusted to driving
at higher speeds, 2) states increased enforcement of driving laws, and 3) automobile
safety was improved. However, we stress that our analysis was not designed to examine
these questions; rather, they are important issues for further investigation.

Statistical Analysis

Each state's rural and urban interstates were analyzed using the structural
modeling approach with deterministic step intervention variables at the time(s) of
the speed-limit increases. Rural interstates are subject to 1987 and 1996 changes,
while urban interstates were only changed around 1996. We will refer to the changes
around 1987 as the FIRST speed-limit increases and those made around 1996 as the
SECOND speed-limit increases.

Results for Individual States

We can summarize the findings as follows:

19 of 40 states experienced a significant increase in fatal crashes along with
the FIRST speed-limit increases on rural interstates (figure 3).

10 of 36 states experienced a significant increase in fatal crashes along with
SECOND speed-limit increases on rural interstates (figure 4).

6 of 31 states experienced a significant increase in fatal crashes along with
the speed-limit increases on urban interstates (figure 5).

Table 1 shows the states with significant changes on rural interstates, the
estimated monthly percentage impact of the speed-limit change, and the numbers of
fatal crashes in 1986 to 1988. From this table, we can see the monthly percentage
increase in the number of fatal crashes attributable to the speed-limit changes.
The numbers of total fatal crashes for 1986 to 1988 are included for two reasons:
1) to interpret the percentages in terms of real numbers and
2) to see if the number of fatal crashes increases in the year after the speed-limit
change. The purpose behind the first reason is to see, without minimizing the value
of human life, what the significant increase translates to in terms of actual number
of crashes. For example, suppose a state averages 36 crashes per year, or 3 per
month, and the estimated monthly increase of fatal crashes is about 33%. The expected
increase in the number of crashes is about one per month. Although statistically
significant, such an increase is small in absolute numbers and may be attributable
to other factors. The purpose behind the second reason is to assess whether drivers
gradually adjust to new driving conditions. For example, Arizona, as graphically
displayed in figure 1, had an increase in the number of crashes the year of the
speed-limit change but a decrease from that level in subsequent years. This
suggests that drivers in Arizona may have learned how to drive safely at the new
limit. Such patterns are not consistent across states, and this issue requires
further investigation.

Table 2 shows the same information for the urban interstates and also includes
1998 data but includes only states that experienced a statistically significant
increase in the number of fatal crashes. During the 1996 set of changes, some states
encountered a negative impact, a decline in the number of fatal crashes after the
speed-limit increase. While this effect may be real, it is difficult to attribute
it to the increase in speed limits. Therefore, the results are not included in table 2.

In order to get an idea of how many fatal crashes are associated with a particular
speed-limit increase, we first remove from the fitted model the term relating to the
increase for those states that had a significant increase in fatal crashes. We then
analyze the difference between the modified expected and actual numbers. We
approximate the predicted number of fatal crashes had the speed limit not increased
by dividing the observed number of fatal crashes by one plus the percent change.
Tables 3
and 4 show this information separated by rural and urban interstates. We
see that the estimated overall percentage increases are of the same order as the
individual increases, resulting in approximately an additional 200 rural and 80 urban
fatal crashes per year. It is important to note that these numbers only represent a
crude approximation of the effect of the speed-limit increase.

Seasonality

One of the powerful benefits of using structural modeling is that instead of
removing seasonality, the effect of a specific month is directly modeled. The
strength of the seasonal pattern was one of the most surprising aspects of this
analysis. Figures 6 and 7 show the following:

29 states exhibited seasonality at the 0.05 level of significance on rural
interstates (figure 6)

18 states exhibited seasonality at the 0.05 level of significance on urban
interstates (figure 7).

The extent of seasonality varies by state. Most states typically have a higher
number of fatal crashes in August. Some states have different patterns with
interpretations unique to that state. For instance, Florida tends to have more fatal
crashes in March on its urban interstates. One possible interpretation of this could
be the increase of traffic from college students traveling to Florida on spring break.
In general, seasonal peaks appear to coincide with peak holiday seasons. Most states do
not produce monthly data on vehicle-miles traveled, so we cannot adjust the data in a
consistent manner for such effects.

Aggregate Analysis

Though the analysis is by state, it is of interest to generalize the effect of
speed limit increases to the nation as a whole. To answer this question, we use
a "Super t-Test." We first record the t-values of the intervention
variables for all states. Positive t-values indicate a positive impact (increase)
of the number of fatal crashes. Of fatal crashes, they determine the significance of the
individual impact of the policy change. To answer the question whether or not fatal
crashes increase along with speed-limit increases, we then perform a
one-sided t-test to determine whether the mean of the t-values of all
of the intervention variables is significantly greater than zero. If we reject the
null hypothesis, we can conclude that there is indeed an increase in the number of
fatal crashes. It does not tell us, however, how large this increase is, only if, on
average, an effect exists.

The Super t-Test for Rural Interstates resulted in a t-statistic of
10.6 with 39 degrees of freedom (one-tailed p-value ≈ 0.000) for the FIRST set
of speed-limit changes and a t-statistic of 4.0 with 36 degrees of freedom
(one-tailed p-value = 0.0002) for the SECOND set of speed-limit changes. For urban
interstates, the Super t-test gave a t-statistic of 1.373 with 30 degrees
of freedom (one-tailed p-value = 0.090). We see from the Super t-Tests that
rural interstates appear to be affected by speed-limit increases, while the effect for
urban interstates is weak.

Conclusion and Future Work

The purpose of the study is to investigate the relationship between speed limits
and traffic-related fatalities. Specifically, we sought to discover if an increase in
the speed limit results in a higher incidence of fatal crashes.

We carried out the data analysis using a time-series technique known as structural
modeling. This approach enables us to partition a series into its level, trend, seasonal,
and irregular (or residual) components and to evaluate the impact of major interventions
such as speed-limit changes. Based on a review of the past literature, we formulated the
impact of a speed-limit change as a one-time percentage increase in the number of accidents,
after which the seasonal and trend patterns in the series would be expected to remain
similar to those of past years. The analysis was performed for each state, separately for
urban and rural interstates. Although the results are statistically significant as noted
above, the numbers in some states may be small. The seasonal patterns probably reflect
changes in the number of vehicle-miles traveled (VMT), with peaks occurring during holiday
seasons. Seasonal analysis is critical to understanding any changes in pattern since
unadjusted comparisons for a few months immediately before and after a change could be
seriously in error. Our analysis allows comparisons to be made after proper adjustment for
seasonal effects. Overall, increases were seen in some states following speed-limit changes.
These increases were predominantly on rural rather than urban interstates.

Acknowledgments

We wish to acknowledge the sponsorship of the Consumers Union for this research.
The views expressed in this paper are those of the authors and are not to be attributed
in any way to the Consumers Union. We also wish to thank Tom Wassel of AstraZeneca, Eric
Falk of Ernst & Young, and Eric Rosenberg of Consumers Union for data collection and
analysis assistance.

Address for Correspondence and End Notes

1 Specifically, only states with increases
between December 8, 1995 and April 1,
1996 are considered.
2 Further information regarding the data and their collection is available from
the author.
3http://www-fars.nhtsa.dot.gov/4 See chapter 13 of Kendall and Ord (1990) or chapter 12 of DeLurgio (1998) for a
description.